The grades on a history midterm at Springer are normally distributed with $\mu = 65$ and $\sigma = 2.5$. Emily earned a $67$ on the exam. Find the z-score for Emily's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Emily's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{67 - {65}}{{2.5}}} $ ${ z \approx 0.80}$ The z-score is $0.80$. In other words, Emily's score was $0.80$ standard deviations above the mean.